{"status": "success", "data": {"description_md": "Each face of a cube is painted either red or blue, each with probability $1/2$. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?\n\n$\\mathrm{(A) \\ } \\frac{1}{4} \\qquad \\mathrm{(B) \\ } \\frac{5}{16} \\qquad \\mathrm{(C) \\ } \\frac{3}{8} \\qquad \\mathrm{(D) \\ } \\frac{7}{16} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}$", "description_html": "<p>Each face of a cube is painted either red or blue, each with probability  <span class=\"katex--inline\">1/2</span> . The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{1}{4} \\qquad \\mathrm{(B) \\ } \\frac{5}{16} \\qquad \\mathrm{(C) \\ } \\frac{3}{8} \\qquad \\mathrm{(D) \\ } \\frac{7}{16} \\qquad \\mathrm{(E) \\ } \\frac{1}{2}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2004 AMC 10B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10B_p24", "prev": "/problem/04_amc10B_p22"}}